Sébastien Gouëzel
Abstract
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We construct a uniformly expanding map of the interval,preserving Lebesgue measure, such that the correspondingtransfer operator admits a spectral gap on the space ofLipschitz functions, but does not act continuously on the spaceof bounded variation functions.
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We construct a uniformly expanding map of the interval,preserving Lebesgue measure, such that the correspondingtransfer operator admits a spectral gap on the space ofLipschitz functions, but does not act continuously on the spaceof bounded variation functions.
Key concepts: Bounded variation, Lipschitz continuity, Bounded function, Mathematics, Interval (graph theory), Lebesgue measure, Bounded deformation, Variation (astronomy)